burgers_diffusion_dg.cc
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#include "rheolef.h"
using namespace rheolef;
using namespace std;
#include "burgers.icc"
#include "burgers_flux_godunov.icc"
#include "runge_kutta_semiimplicit.icc"
#include "burgers_diffusion_exact.h"
#undef NEUMANN
#include "burgers_diffusion_operators.icc"
int main(int argc, char**argv) {
environment rheolef (argc, argv);
geo omega (argv[1]);
space Xh (omega, argv[2]);
size_t k = Xh.degree();
Float epsilon = (argc > 3) ? atof(argv[3]) : 0.1;
size_t nmax = (argc > 4) ? atoi(argv[4]) : 500;
Float tf = (argc > 5) ? atof(argv[5]) : 1;
size_t p = (argc > 6) ? atoi(argv[6]) : min(k+1,rk::pmax);
Float delta_t = tf/nmax;
size_t d = omega.dimension();
Float beta = (k+1)*(k+d)/Float(d);
trial u (Xh); test v (Xh);
form m = integrate (u*v);
integrate_option iopt;
iopt.invert = true;
form inv_m = integrate (u*v, iopt);
form a = epsilon*(
integrate (dot(grad_h(u),grad_h(v)))
#ifdef NEUMANN
+ integrate ("internal_sides",
#else // NEUMANN
+ integrate ("sides",
#endif // NEUMANN
beta*penalty()*jump(u)*jump(v)
- jump(u)*average(dot(grad_h(v),normal()))
- jump(v)*average(dot(grad_h(u),normal()))));
vector<problem> pb (p+1);
for (size_t i = 1; i <= p; ++i) {
form ci = m + delta_t*rk::alpha[p][i][i]*a;
pb[i] = problem(ci);
}
vector<field> uh(p+1, field(Xh,0));
uh[0] = interpolate (Xh, u_init(epsilon));
branch even("t","u");
dout << catchmark("epsilon") << epsilon << endl
<< even(0,uh[0]);
for (size_t n = 0; n < nmax; ++n) {
Float tn = n*delta_t;
Float t = tn + delta_t;
field uh_next = uh[0] - delta_t*rk::tilde_beta[p][0]*(inv_m*gh(epsilon, tn, uh[0], v));
for (size_t i = 1; i <= p; ++i) {
Float ti = tn + rk::gamma[p][i]*delta_t;
field rhs = m*uh[0] - delta_t*rk::tilde_alpha[p][i][0]*gh(epsilon, tn, uh[0], v);
for (size_t j = 1; j <= i-1; ++j) {
Float tj = tn + rk::gamma[p][j]*delta_t;
rhs -= delta_t*( rk::alpha[p][i][j]*(a*uh[j] - lh(epsilon,tj,v))
+ rk::tilde_alpha[p][i][j]*gh(epsilon, tj, uh[j], v));
}
rhs += delta_t*rk::alpha[p][i][i]*lh (epsilon, ti, v);
pb[i].solve (rhs, uh[i]);
uh_next -= delta_t*(inv_m*( rk::beta[p][i]*(a*uh[i] - lh(epsilon,ti,v))
+ rk::tilde_beta[p][i]*gh(epsilon, ti, uh[i], v)));
}
uh_next = limiter(uh_next);
dout << even(tn+delta_t,uh_next);
uh[0] = uh_next;
}
}
burgers.icc
The Burgers equation – the f function.
main
int main(int argc, char **argv)
Definition: burgers_diffusion_dg.cc:34
burgers_diffusion_exact.h
The diffusive Burgers equation – its exact solution.
u_init
u_exact u_init
Definition: burgers_diffusion_exact.h:32
burgers_diffusion_operators.icc
The diffusive Burgers equation – operators.
lh
field lh(Float epsilon, Float t, const test &v)
Definition: burgers_diffusion_operators.icc:25
gh
field gh(Float epsilon, Float t, const field &uh, const test &v)
Definition: burgers_diffusion_operators.icc:37
burgers_flux_godunov.icc
The Burgers equation – the Godonov flux.
Float
see the Float page for the full documentation
branch
see the branch page for the full documentation
field
see the field page for the full documentation
form
see the form page for the full documentation
geo
see the geo page for the full documentation
rheolef::catchmark
see the catchmark page for the full documentation
Definition: catchmark.h:67
rheolef::environment
see the environment page for the full documentation
Definition: environment.h:115
rheolef::integrate_option
see the integrate_option page for the full documentation
Definition: integrate_option.h:125
rheolef::integrate_option::invert
bool invert
Definition: integrate_option.h:168
rheolef::std
Definition: vec_expr_v2.h:402
rheolef::problem
problem_basic< Float > problem
Definition: problem.h:163
rheolef::Float
double Float
see the Float page for the full documentation
Definition: Float.h:143
rheolef::dout
odiststream dout(cout)
see the diststream page for the full documentation
Definition: diststream.h:430
rheolef::field
field_basic< Float > field
see the field page for the full documentation
Definition: field.h:419
space
see the space page for the full documentation
test
see the test page for the full documentation
trial
see the test page for the full documentation
mkgeo_ball.d
int d
Definition: mkgeo_ball.sh:154
mkgeo_ball.n
int n
Definition: mkgeo_ball.sh:150
mkgeo_ball.a
int a
Definition: mkgeo_ball.sh:151
mkgeo_sector.m
m
Definition: mkgeo_sector.sh:118
rheolef
This file is part of Rheolef.
Definition: compiler_eigen.h:37
rheolef::limiter
field_basic< T, M > limiter(const field_basic< T, M > &uh, const T &bar_g_S, const limiter_option &opt)
see the limiter page for the full documentation
Definition: limiter.cc:65
rheolef::dot
rheolef::std enable_if ::type dot const Expr1 expr1, const Expr2 expr2 dot(const Expr1 &expr1, const Expr2 &expr2)
dot(x,y): see the expression page for the full documentation
Definition: vec_expr_v2.h:415
rheolef::grad_h
std::enable_if< details::is_field_convertible< Expr >::value,details::field_expr_v2_nonlinear_terminal_field< typename Expr::scalar_type,typename Expr::memory_type,details::differentiate_option::gradient >>::type grad_h(const Expr &expr)
grad_h(uh): see the expression page for the full documentation
Definition: field_expr_terminal.h:949
rheolef::integrate
std::enable_if< details::is_field_expr_v2_nonlinear_arg< Expr >::value &&! is_undeterminated< Result >::value, Result >::type integrate(const geo_basic< T, M > &omega, const Expr &expr, const integrate_option &iopt, Result dummy=Result())
see the integrate page for the full documentation
Definition: integrate.h:202
rheolef::interpolate
field_basic< T, M > interpolate(const space_basic< T, M > &V2h, const field_basic< T, M > &u1h)
see the interpolate page for the full documentation
Definition: interpolate.cc:233
rheolef::penalty
details::field_expr_v2_nonlinear_terminal_function< details::penalty_pseudo_function< Float > > penalty()
penalty(): see the expression page for the full documentation
Definition: field_expr_terminal.h:626
rheolef::normal
details::field_expr_v2_nonlinear_terminal_function< details::normal_pseudo_function< Float > > normal()
normal: see the expression page for the full documentation
Definition: field_expr_terminal.h:439
rk::tilde_alpha
Float tilde_alpha[][pmax+1][pmax+1]
Definition: runge_kutta_semiimplicit.icc:48
rk::tilde_beta
Float tilde_beta[][pmax+1]
Definition: runge_kutta_semiimplicit.icc:65
rk::gamma
Float gamma[][pmax+1]
Definition: runge_kutta_semiimplicit.icc:70
rk::beta
Float beta[][pmax+1]
Definition: runge_kutta_semiimplicit.icc:60
rk::alpha
Float alpha[][pmax+1][pmax+1]
Definition: runge_kutta_semiimplicit.icc:36
rk::pmax
constexpr size_t pmax
Definition: runge_kutta_semiimplicit.icc:27
rheolef.h
rheolef - reference manual
runge_kutta_semiimplicit.icc
The semi-implicit Runge-Kutta scheme – coefficients.
a
Definition: diffusion_isotropic.h:25
p
Definition: sphere.icc:25
u
Definition: leveque.h:25
u
Float u(const point &x)
Definition: transmission_error.cc:26
epsilon
Float epsilon
Definition: transmission_error.cc:25